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Process Control: Modeling, Design, and Simulation by B. Wayne Bequette

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7.5. Bode and Nyquist Stability

In the previous section we used a thought experiment based on the open-loop (controller + process) response to a sinusoidal setpoint input. We found that if the amplitude ratio of the open-loop transfer function [gc(s)gp(s)] is less than 1 when the phase angle is −180°, then the system will be stable when the loop is closed. This requirement is also known as the Bode stability criterion. Notice that we are assuming no valve and measurement effects [or lumping them into gp(s)]. If these effects are included, then gc(s)gp(s)gv(s)gm(s) should be used in the analysis.

Bode Stability Criterion

Assume that the process is stable [gp(s) has no poles in the RHP] and the controller is stable [gc(s) has no poles in the RHP]. ...

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